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  • A set is a collection of well defined objects.
  • A set which does not contain any element is called an empty set.
  • A set with definite number of elements is called finite set and if not it is called infinite set.
  • Two sets are said to be equal if they have exactly the same elements.
  • Set A is said to be subset of set B, if every element of the set A is also an element of the set B. Intervals are subsets of R.
  • A power set of a set A is the collection of all the subsets of the set A. It is denoted as P(A).
  • The set of all the elements which are either in A or in B is the union of two sets A and B.
  • The set of all elements which are common in both the sets A and B is the intersection of the two sets.
  • The set A - B is the set of all elements in A but not in B.
  • The complement of a subset A of universal set U, denoted as A' is the set of all elements of U which are not the elements of A.
  • (A  B)' = A'  B' and (A  B)' = A'  B' for any two sets A and B.
  • If A and B are finite sets such that A  B = φ, n(A  B) = n(A) + n (B). If A and B are not disjoint sets, n(A  B) = n(A) + n (B) - n(A  B).

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